State the maximum or minimum value of the
function, and state whether it is a maximum
or a minimum.

f (x) = x^2 − 8x + 21

Question

State the maximum or minimum value of the
function, and state whether it is a maximum
or a minimum.

f (x) = x^2 − 8x + 21

anonymous · Answer

how do you do these?

ranga · Answer

Using Calculus?

anonymous · Answer

no its for quadratic functions

ranga · Answer

Okay.  From what we discussed earlier this is a quadratic function which is a parabola.  The "a" is positive so it opens upward which means it will have a minimum because of the U shape.  So you need to find the vertex.

The x coordinate of the vertex is -b/2a.

So just plug in the values for a and b and find the x coordinate of the vertex.

anonymous · Answer

ohhh that's simple you must really be a math professor because you are very good at teaching

ranga · Answer

oh thank you.  I am not a prof though.

anonymous · Answer

is the min the one that opens upward?

ranga · Answer

Yes.  You can visualize a U.  It has the lowest y value at the vertex and therefore it is a minimum.  If it is an inverted U then the maximum value will be at the top.

Once you find the x value of the vertex you need to put that into f(x) and find the y value which is the minimum value they are asking for

ranga · Answer

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